The Canonical Bijection Between Pipe Dreams and Bumpless Pipe Dreams

Abstract

We present a direct bijection between reduced pipe dreams and reduced bumpless pipe dreams by interpreting reduced compatible sequences on bumpless pipe dreams and show that this bijection preserves Monk's formula, establishing its canonical nature.

arXiv comment27 pages, 25 figures

References in corpus (5)

• Back stable Schubert calculus
• Double Grothendieck polynomials and colored lattice models
• Schubert Products for Permutations with Separated Descents
• Frozen Pipes: Lattice Models for Grothendieck Polynomials
• Bijective Proofs of Monk's rule for Schubert and Double Schubert Polynomials with Bumpless Pipe Dreams

Cited by in corpus (3)

• A pipe dream perspective on totally symmetric self-complementary plane partitions
• Hybrid Pipe Dreams for Key Polynomials
• Quantum bumpless pipe dreams